Subgroups — #20256791

Order 6016.

996 conjugacy classes of subgroups.

The subgroup lattice has 250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689753	C₂	1	4	yes	maximal, complemented
2	#15689752	C₂	1	4	yes	maximal, complemented
3	#15689750	C₂	1	4	yes	maximal, complemented
4	#15689748	C₂	1	4	yes	maximal
5	#15689680	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689677	C₂	1	8	yes	maximal, complemented
7	#15689676	C₂	1	2	yes	maximal, complemented
8	C₂×#13093981	C₂	1	1	yes	maximal, characteristic
9	#117×D₄₇	C₂	1	2	yes	maximal
10	C₄₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
12	#13094024	C₂²	1	2	yes	complemented
13	#13094023	C₂²	1	4	yes	complemented
14	#13094023	C₂²	1	8	yes	complemented
15	#13094022	C₂²	1	8	yes	complemented
16	#13094016	C₂²	1	2	yes	complemented
17	#13094015	C₂²	1	4	yes	complemented
18	#13094014	C₂²	1	8	yes	complemented
19	#13094014	C₂²	1	8	yes	complemented
20	#13094004	C₂²	1	8	yes	—
21	#13094003	C₂²	1	4	yes	—
22	#13094002	C₂²	1	8	yes	—
23	#13094002	C₂²	1	8	yes	—
24	#13094001	C₂²	1	8	yes	—
25	#13094000	C₂²	1	8	yes	—
26	C₄×Dic₉₄	C₂²	1	8	yes	complemented
27	C₄×Dic₉₄	C₂²	1	4	yes	complemented
28	#13093983	C₂²	1	2	yes	—
29	#13093982	C₂²	1	4	yes	—
30	#13093981	C₂²	1	2	yes	—
31	#13093981	C₂²	1	2	yes	—
32	#13093981	C₂²	1	4	yes	—
33	#13093981	C₂²	1	4	yes	—
34	#13093980	C₂²	1	4	yes	—
35	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
36	C₄⋊C₄×D₄₇	C₂²	1	4	yes	—
37	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
38	C₂²⋊C₄×D₄₇	C₂²	1	4	yes	—
39	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
40	C₄²×D₄₇	C₂²	1	4	yes	—
41	C₄⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
42	#125×C₄₇	C₂²	1	2	yes	complemented
43	C₂²⋊Q₈×C₄₇	C₂²	1	4	yes	—
44	C₄×Q₈×C₄₇	C₂²	1	4	yes	complemented
45	#117×C₄₇	C₂²	1	2	yes	—
46	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
47	C₂³×D₄₇	C₂³	1	1	yes	characteristic
48	C₂×Q₈×C₄₇	C₂³	1	4	yes	—
49	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
50	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
51	C₂²×Dic₄₇	C₂³	1	2	yes	—
52	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
53	C₂×C₄×D₄₇	Q₈	1	8	yes	complemented
54	C₂×C₄×D₄₇	C₂³	1	8	yes	—
55	C₂×C₄×D₄₇	C₂³	1	2	yes	—
56	C₂×C₄×D₄₇	C₂³	1	2	yes	—
57	C₂×Dic₉₄	C₂³	1	8	yes	—
58	C₂×Dic₉₄	C₂³	1	4	yes	—
59	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
60	C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
61	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
62	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
63	C₄²×C₄₇	C₂³	1	2	yes	—
64	C₄²×C₄₇	C₂³	1	1	yes	characteristic
65	C₄²×C₄₇	C₂³	1	1	yes	characteristic
66	C₄²×C₄₇	C₂³	1	4	yes	—
67	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
68	(C₂×D₄₇)⋊C₄	C₂³	1	8	yes	—
69	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
70	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
71	C₄⋊Dic₄₇	C₂³	1	4	yes	—
72	C₄⋊Dic₄₇	C₂³	1	8	yes	—
73	C₄⋊Dic₄₇	C₂³	1	4	yes	—
74	Dic₄₇⋊C₄	C₂³	1	8	yes	—
75	Dic₄₇⋊C₄	C₂³	1	4	yes	—
76	Dic₄₇⋊C₄	C₂³	1	4	yes	—
77	Dic₄₇⋊C₄	C₂³	1	8	yes	—
78	Dic₄₇⋊C₄	C₂³	1	8	yes	—
79	Dic₄₇⋊C₄	C₂³	1	8	yes	—
80	C₄×Dic₄₇	C₂³	1	8	yes	—
81	C₄×Dic₄₇	C₂³	1	4	yes	—
82	C₄×Dic₄₇	C₂³	1	2	yes	—
83	C₄×Dic₄₇	C₂³	1	2	yes	—
84	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
85	C₂²×D₄₇	—	4	2	no	—
86	C₂²×D₄₇	C₂×Q₈	1	4	yes	—
87	C₂²×D₄₇	C₂⁴	1	2	yes	—
88	Q₈×C₄₇	—	4	4	no	—
89	C₂×C₄×C₄₇	—	4	2	no	—
90	C₂×C₄×C₄₇	C₂×Q₈	1	4	yes	—
91	C₂×C₄×C₄₇	C₂⁴	1	8	yes	—
92	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
93	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
94	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
95	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
96	C₂×Dic₄₇	—	4	2	no	—
97	C₂×Dic₄₇	C₂×Q₈	1	4	yes	—
98	C₂×Dic₄₇	C₂⁴	1	4	yes	—
99	C₂×Dic₄₇	C₂⁴	1	8	yes	—
100	C₂×Dic₄₇	C₂⁴	1	2	yes	—
101	C₄×D₄₇	—	4	8	no	—
102	C₄×D₄₇	C₂×Q₈	1	8	yes	—
103	C₄×D₄₇	C₂×Q₈	1	8	yes	—
104	Dic₉₄	—	4	4	no	—
105	Dic₉₄	—	4	8	no	—
106	C₂²×C₄₇	—	2	2	no	—
107	C₂²×C₄₇	C₂²×Q₈	1	2	yes	—
108	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
109	C₂×D₄₇	—	2	4	no	—
110	C₂×D₄₇	—	4	4	no	—
111	C₂×D₄₇	C₂²×Q₈	1	4	yes	—
112	C₄×C₄₇	—	2	2	no	—
113	C₄×C₄₇	—	2	8	no	—
114	C₄×C₄₇	—	2	2	no	—
115	C₄×C₄₇	C₂²×Q₈	1	2	yes	—
116	C₄×C₄₇	C₂²×Q₈	1	2	yes	—
117	Dic₄₇	—	2	8	no	—
118	Dic₄₇	—	2	4	no	—
119	Dic₄₇	C₂²×Q₈	1	4	yes	—
120	#3458	—	47	1	no	maximal, Sylow
121	C₂×C₄₇	—	2	2	no	—
122	C₂×C₄₇	C₂³×Q₈	1	1	yes	characteristic
123	C₂×C₄₇	#585	1	2	yes	—
124	D₄₇	—	2	4	no	—
125	#544	—	47	4	no	—
126	#544	—	47	4	no	—
127	#544	—	47	4	no	—
128	#543	—	47	4	no	—
129	#533	—	47	8	no	—
130	#533	—	47	2	no	—
131	#533	—	47	1	no	—
132	#533	D₄₇	1	1	yes	characteristic, complemented
133	C₂×#117	—	47	2	no	—
134	C₂×#117	—	47	1	no	—
135	C₄₇	#3458	1	1	yes	characteristic, complemented, Sylow
136	C₂³×C₄	—	47	1	no	—
137	C₄⋊Q₈	—	47	8	no	—
138	C₄⋊Q₈	—	47	8	no	—
139	C₄⋊Q₈	—	47	4	no	—
140	C₄⋊Q₈	—	47	2	no	—
141	C₄⋊Q₈	C₂×D₄₇	1	2	yes	complemented
142	#125	—	47	8	no	—
143	#125	—	47	8	no	—
144	#125	—	47	4	no	—
145	#125	—	47	2	no	—
146	#125	C₂×D₄₇	1	2	yes	complemented
147	C₂²⋊Q₈	—	47	8	no	—
148	C₂²⋊Q₈	—	47	4	no	—
149	C₂²⋊Q₈	—	47	8	no	—
150	C₂²⋊Q₈	—	47	8	no	—
151	C₂²⋊Q₈	—	47	8	no	—
152	C₂²⋊Q₈	—	47	8	no	—
153	C₂²⋊Q₈	C₂×D₄₇	1	4	yes	—
154	C₄×Q₈	—	47	8	no	—
155	C₄×Q₈	—	47	4	no	—
156	C₄×Q₈	C₂×D₄₇	1	4	yes	complemented
157	#117	—	47	2	no	—
158	#117	—	47	4	no	—
159	#117	—	47	4	no	—
160	#117	—	47	4	no	—
161	#117	—	47	4	no	—
162	#117	—	47	2	no	—
163	#117	—	47	2	no	—
164	#117	C₂×D₄₇	1	2	yes	—
165	C₂×C₄⋊C₄	—	47	2	no	—
166	C₂×C₄⋊C₄	—	47	4	no	—
167	C₂×C₂²⋊C₄	—	47	2	no	—
168	C₂×C₂²⋊C₄	—	47	4	no	—
169	C₂×C₄²	—	47	1	no	—
170	C₂×C₄²	—	47	4	no	—
171	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
172	C₂⁴	—	47	1	no	—
173	C₂×Q₈	—	47	8	no	—
174	C₂×Q₈	—	47	4	no	—
175	C₂×Q₈	C₂²×D₄₇	1	4	yes	—
176	C₂²×C₄	—	47	1	no	—
177	C₂²×C₄	—	47	8	no	—
178	C₂²×C₄	—	47	2	no	—
179	C₂²×C₄	—	47	2	no	—
180	C₂²×C₄	—	47	2	no	—
181	C₂²×C₄	—	47	8	no	—
182	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
183	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
184	C₄⋊C₄	—	47	8	no	—
185	C₄⋊C₄	—	47	4	no	—
186	C₄⋊C₄	—	47	4	no	—
187	C₄⋊C₄	—	47	8	no	—
188	C₄⋊C₄	—	47	8	no	—
189	C₄⋊C₄	—	47	8	no	—
190	C₄⋊C₄	—	47	4	no	—
191	C₄⋊C₄	—	47	8	no	—
192	C₄⋊C₄	—	47	4	no	—
193	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
194	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
195	C₄⋊C₄	C₂²×D₄₇	1	8	yes	—
196	C₂²⋊C₄	—	47	4	no	—
197	C₂²⋊C₄	—	47	8	no	—
198	C₂²⋊C₄	—	47	4	no	—
199	C₂²⋊C₄	—	47	4	no	—
200	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
201	C₄²	—	47	8	no	—
202	C₄²	—	47	2	no	—
203	C₄²	—	47	4	no	—
204	C₄²	—	47	2	no	—
205	C₄²	C₂²×D₄₇	1	1	yes	characteristic
206	C₄²	C₂²×D₄₇	1	1	yes	characteristic
207	C₄²	C₂²×D₄₇	1	4	yes	—
208	C₄²	C₂²×D₄₇	1	2	yes	—
209	C₂³	—	47	2	no	—
210	C₂³	—	47	4	no	—
211	C₂³	—	188	2	no	—
212	C₂³	C₂³×D₄₇	1	1	yes	characteristic
213	Q₈	—	4	4	no	—
214	Q₈	—	188	4	no	—
215	Q₈	—	188	8	no	—
216	C₂×C₄	—	4	2	no	—
217	C₂×C₄	—	47	4	no	—
218	C₂×C₄	—	47	2	no	—
219	C₂×C₄	—	47	8	no	—
220	C₂×C₄	—	47	8	no	—
221	C₂×C₄	—	47	4	no	—
222	C₂×C₄	—	47	8	no	—
223	C₂×C₄	—	188	8	no	—
224	C₂×C₄	—	188	2	no	—
225	C₂×C₄	Q₈×D₄₇	1	4	yes	—
226	C₂×C₄	C₂³×D₄₇	1	8	yes	—
227	C₂×C₄	C₂³×D₄₇	1	2	yes	—
228	C₂×C₄	C₂³×D₄₇	1	2	yes	—
229	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
230	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
231	C₂²	—	2	2	no	—
232	C₂²	—	47	4	no	—
233	C₂²	—	94	4	no	—
234	C₂²	—	188	4	no	—
235	C₂²	C₂×Q₈×D₄₇	1	2	yes	—
236	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
237	C₄	—	2	2	no	—
238	C₄	—	2	2	no	—
239	C₄	—	2	8	no	—
240	C₄	—	47	4	no	—
241	C₄	—	94	8	no	—
242	C₄	—	94	4	no	—
243	C₄	C₂×Q₈×D₄₇	1	2	yes	—
244	C₄	C₂×Q₈×D₄₇	1	2	yes	—
245	C₂	—	2	2	no	—
246	C₂	—	94	4	no	—
247	C₂	C₂²×Q₈×D₄₇	1	1	yes	characteristic
248	C₂	#15689959	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂³×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Frattini	C₂²	C₂⁴×D₄₇
Fitting	C₄₇×#533	C₂
hypercenter	#533	D₄₇
hypocenter	C₄₇	#3458
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #533

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #15689753	C₂	semidirect
2. #15689752	C₂	semidirect
3. #15689750	C₂	semidirect
5. #15689680	C₂	semidirect
6. #15689677	C₂	semidirect
7. #15689676	C₂	semidirect
10. C₄₇×#533	C₂	semidirect
12. #13094024	C₂²	semidirect
13. #13094023	C₂²	semidirect
14. #13094023	C₂²	semidirect
15. #13094022	C₂²	semidirect
16. #13094016	C₂²	semidirect
17. #13094015	C₂²	semidirect
18. #13094014	C₂²	semidirect
19. #13094014	C₂²	semidirect
26. C₄×Dic₉₄	C₂²	semidirect
27. C₄×Dic₉₄	C₂²	semidirect
41. C₄⋊Q₈×C₄₇	C₂²	semidirect
42. #125×C₄₇	C₂²	semidirect
44. C₄×Q₈×C₄₇	C₂²	semidirect
53. C₂×C₄×D₄₇	Q₈	semidirect
132. #533	D₄₇	semidirect
135. C₄₇	#3458	semidirect
141. C₄⋊Q₈	C₂×D₄₇	semidirect
146. #125	C₂×D₄₇	semidirect
156. C₄×Q₈	C₂×D₄₇	semidirect